First, the practice of assigning opus numbers was not very common in
Mozart's times. Only a handful of Mozart's works have opus numbers.
Second, Mozart is not really very special in this respect. There is
practically no major or semi-major composer whose works haven't been
by now catalogued and in most cases assigned a catalog number. Mozart's
cataloguer was L. A. von Koechel, that's why you see a "K". The reasons
that using "K" is so common are: 1) there are so many of his works of the
same genre and key that some way of distinguishing one from another is
needed; 2) the Koechel catalog was probably the first scholarly catalog
(in the modern sense) of works of any composer; 3) Koechel's numbering
has been in common use for the last 160 years, and people got used to it.
Bach's works are nowadays preceded by "BWV", for instance; Haydn's by "Hob".
-Margaret